When a reliable design is to be achieved screw joints are such designed that
the effective cross section area is determinative for the strength of the
assembly, i.e. the screw fails rather than the internal or external thread
strips. The length of the screw engagement should at least be sufficient to
carry the full load necessary to break the screw. If not, thread stripping
starts at the first engaged thread and successively shears off subsequent
threads. This may take some hours to complete and so the joint may appear
fine at the time of assembly but will fail in service.

The size of a
screwed fastener is first to be established by calculating the required
tensile area with the appropriate factor of safety. If the joint is fixed
using a nut and bolt from the same grade there is no need to size the nut
while the standard length of the nut is such sized that the screw will fail
before the thread is stripped. If the screw fastens into a tapped hole of
a low strength material then a check of the thread engagement length is
required.

The shear strength is defined by Fs=τ Ath where τ = shear strength of the
material and Ath the thread shear area. When the external and internal
thread are
of the same material, the internal thread (in the tapped hole) is stronger
in shear than the external thread. One of the problems in predicting the thread stripping strength is
that without considering such effects as thread bending, nut dilation
(effect of radial displacement) and tolerances of thread dimensions an
optimistic result is calculated.

Accurately calculating the required thread engagement length is a complex
problem. In an attempt to ensure that thread stripping does not occur rigorous
and extensive tests can be fulfilled in which the strength is measured of a
range of engagement lengths. In a similar way the length of engagement
Le=0.75d of a standard nut is defined (standard nut height 0.8d>0.75d
because of the chamfered hole).

The shear strength of a material is often expressed in the ratio of the
shear to tensile strength, for ductile materials like steel τ/σ=0.580.
With a bolt and nut of the same grade the ratio Ath/As should exceed 0.580
to ensure that the strength of the tensile area is the weakest. The
stripping strength of a particular engagement length or material can be
derived from the standard nut height. A material with only the half shear
strength of the fastener requires the double length of engagement,
Le=2x0.75d.

Weak materials are sensitive for galling at high contact pressure. In
order to enlarge the stripping strength and at the same time to prevent
galling it is possible to use helicoils.

Case: Effective length of thread engagement

Problem: Calculate the required length of engagement of a tapped hole in a
casting of spheroidal graphite cast iron. The thread strength must be able
to carry the full load at which a M12-10.9 bolt fails.

Given: The tolerance class of the dimensions of a standard nut are assumed
to be representative for the tapped hole. The ratio of shear strength to
tensile strength of the SG cast iron is taken as τ/σ=0.9, where the tensile
strength is σ=500 MPa.

Accurately calculating the required thread engagement length with a
sophisticated program available at
www.boltscience.com , in which a large number of influence factors are
considered, finally results in a required effective thread engagement length
of 12.9 mm.

A generally used practical calculation method for the tread
stripping strength is given by the formula Ath=0.5πd0L0.
where d0=(d2+d3)/2.
Applying this formula results in the effective length of thread engagement
of L0=11.5mm.

Note that the shear strength of a metric fine
thread exceeds that of a standard metric thread because of the slightly
larger d0-value (approximately 6%).